System and method for determining spin measurements using ball marking

ABSTRACT

A sports ball is configured to enhance detection of spin properties by radar. The ball includes a spherical body having a first reflectivity with respect to radiation generated by a radar to be used in detecting spin of the ball. In addition, the ball includes a plurality of markers. Each of the markers has a second reflectivity with respect to the radiation generated by a radar to be used in detecting spin of the ball. The second reflectivity is different from the first reflectivity. The markers are distributed on the ball so that every great circle extending around an exterior surface of the ball is within a distance d of a projection on the exterior surface of the ball of at least one of the markers. The distance d is less than a radius of the ball.

PRIORITY CLAIM

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 62/873,105 filed Jul. 11, 2019, U.S. Provisional PatentApplication Ser. No. 62/913,523 filed 10 Oct. 10, 2019, and U.S.Provisional Patent Application Ser. No. 62/970,394 filed Feb. 5, 2020.The specifications of the above-identified applications are incorporatedherewith by reference.

FIELD

The present disclosure relates to a system and a method for determiningspin characteristics of a sports ball with reflective markings.

BACKGROUND

Spin parameters such as the spin rate and orientation of the spin axisof a sports ball are highly useful both for tracking sports balls, forsimulating the flight of sports balls and for developing sportsequipment such as sports balls, clubs, irons, rackets, bats or the likeused for launching sports balls. Such determinations may be made basedon the signature in radar data corresponding to the spinning ball.

U.S. Pat. No. 8,845,442 discloses a method for determining the spin rateof a sports ball by analyzing the modulation of a Doppler radar signalof a spinning ball in flight. However, the modulation signal using thismethod is relatively weak. In situations where data is available onlyfor a very short ball flight, such as in an indoor golf setup, themodulation signal of an unmarked ball is often too weak to be useful fora spin rate measurement.

To amplify the modulation signal and make spin detection possible inthese situations, reflective markers may be placed on the ball. However,to generate useful data, prior systems often required that thereflective marker be oriented precisely before launching the ball and inmany cases, systems would be required to have exact a priori knowledgeabout the marking pattern. For example, the marker may be required to beoriented directly facing the radar device during its flight. Theseorientation limitation for the ball may inhibit the user friendliness ofthe system, and useful data may not be generated for ball trajectorieswhen the ball is launched differently than intended.

The current embodiments describe a method and apparatus for determiningspin characteristics of a ball, such as spin rate and orientation ofspin axis, by applying contrast regions to the ball with a specificpositioning requirement in such a way, that no matter the orientation ofthe spin axis and position of the radar antennas, no matter theorientation of the ball and without requiring any knowledge about thespecific positioning geometry of the contrast regions, the spincharacteristics can be determined from the modulation of received radarsignal(s).

SUMMARY

The present disclosure relates to a sports ball configured to enhancedetection of spin properties by a radar. The ball includes a sphericalbody having a first reflectivity with respect to radiation generated bythe radar to be used in detecting spin of the ball; and a plurality ofmarkers, each of the markers having a second reflectivity with respectto the radiation generated by a radar to be used in detecting spin ofthe ball, the second reflectivity being different from the firstreflectivity. The markers are distributed on the ball so that everygreat circle extending around an exterior surface of the ball is withina distance d of a projection on the exterior surface of the ball of atleast one of the markers. The distance d is less than a radius of theball.

In an embodiment, the markers are circular and the projection on theexterior surface of the ball of each marker comprises a cone extendingfrom a center of the ball to the exterior surface of the ballcircumscribing the marker.

In an embodiment, at least one of the markers is a planar disc embeddedwithin the sports ball.

In an embodiment, at least one of the markers is a portion of aspherical surface within the ball circumscribed by a circle, thespherical surface having the same center as the ball.

In an embodiment, the markers are rectangular and the projection on theexterior surface of the ball of each marker comprises a pyramidextending from a center of the ball to the exterior surface of the ballcircumscribing the marker.

In an embodiment, at least one of the markers is a planar rectangleembedded within the sports ball.

In an embodiment, at least one of the markers is a portion of aspherical surface within the ball circumscribed by a pyramid extendingfrom a center of the ball to the exterior surface of the ball.

In an embodiment, when more than one marker is within the distance d ofa great circle, the projections of all of these markers on the exteriorsurface of the ball are unequally distributed about the great circle.

In an embodiment, there are only two markers within the distance d of afirst one of the great circles, these markers are not diametricallyopposed to one another.

In an embodiment, the two markers are not diametrically opposed to oneanother within a predetermined tolerance.

In an embodiment, the markers within the distance d of the great circleare separated from positions of equal distribution about the greatcircle by at least a distance m from the projections onto the exteriorsurface of the ball of every other marker whose projection is within thedistance d of the great circle.

In an embodiment, the diametrically opposed position of each marker is aportion of the exterior surface of the ball diametrically opposed to theprojection of the marker onto the exterior surface of the ball, whereinthe diametrically opposed position for each marker has the same size andshape as the projection of the corresponding marker onto the exteriorsurface of the ball.

In an embodiment, at least a portion of each of the markers extendswithin a single hemisphere of the ball.

The present disclosure also relates to a sports ball configured toenhance detection of spin properties by a radar. The ball includes aspherical body having a first reflectivity with respect to radiationgenerated by the radar to be used in detecting spin of the ball; and aspherical layer within the ball of a material having a secondreflectivity with respect to the radiation generated by a radar to beused in detecting spin of the ball, the second reflectivity beingdifferent from the first reflectivity, a plurality of markers formedwithin the layer at which the material of the layer is not present sothat the markers have the first reflectivity. The markers aredistributed on the ball so that every great circle extending around anexterior surface of the ball is within a distance d of a projection onthe exterior surface of the ball of at least one of the markers. Thedistance d is less than a radius of the ball.

In addition, the present disclosure relates to a method formanufacturing a sports ball configured to enhance detection of spinproperties by a radar. The method includes forming a spherical bodyhaving a first reflectivity with respect to radiation generated by theradar to be used in detecting spin of the ball; and forming on thesports ball a plurality of markers, each of the markers having a secondreflectivity with respect to the radiation generated by a radar to beused in detecting spin of the ball, the second reflectivity beingdifferent from the first reflectivity. The markers are distributed onthe ball so that every great circle extending around an exterior surfaceof the ball is within a distance d of a projection on the exteriorsurface of the ball of at least one of the markers. The distance d isless than a radius of the ball.

BRIEF DESCRIPTION

FIG. 1a shows a first marked ball with a great circle surrounded by bandof width 2d drawn thereon that satisfies the positioning requirement.

FIG. 1b shows a second marked ball with a great circle surrounded by aband of width 2d drawn thereon that does not satisfy the positioningrequirement.

FIG. 1c shows a top view of a third marked ball having multiple markerscontacting a band of width 2d surrounding the same great circle andsatisfying an optional additional positioning constraint.

FIG. 1d shows a top view of a fourth marked ball having multiple markerscontacting a band of width 2d surrounding the same great circle andwhich does not satisfy the additional positioning constraint.

FIGS. 2a-b show a marked ball with a first marking pattern according toone embodiment of the present disclosure.

FIGS. 3a-b show a marked ball with a second marking pattern according toone embodiment of the present disclosure.

FIG. 4 shows a system for determining a spin axis of a sports ballaccording to an exemplary embodiment of the present invention.

FIG. 5 shows an exemplary method for determining the spin axis of aspinning golf ball according to an exemplary embodiment of the presentinvention.

DETAILED DESCRIPTION

The exemplary embodiments may be further understood with reference tothe following description and the related appended drawings, whereinlike elements are provided with the same reference numerals. Theexemplary embodiments relate to a system and method for radar-baseddeterminations of spin characteristics of a sports ball, where theexemplary sports ball is modified by incorporating markers having anelectrical reflectivity different from other areas of the ball. Thereflective markers provide a contrast region on the surface (or close tothe surface) of the ball that may be detected in radar data. Forexample, the markers may be electrically conductive in the frequencyregion of the radar being used in the flight trajectory measurementsystem so that microwave radiation transmitted by the radar is reflectedand received differently by the markers than the radiation impactingother portions of the ball. Specific positioning constraints for themarkers are described below, that permit the detection of the markersregardless of the orientation of the axis about which the ball isspinning relative to the radar.

Although exemplary embodiments detailed herein describe golf balls orbaseballs having these markings, those skilled in the art willunderstand that any sports balls or even non-sports related objects maybe marked and have spin characteristics determined in the same manner.The exemplary embodiments may be applicable to any spherical orsubstantially spherical ball. For example, although a golf ball may begenerally spherical, the outer surface of the ball may include dimples,one or more seams or other surface irregularities and a baseball mayhave raised seams. However, for present purposes these balls may beassumed to be generally spherical.

Although markings distributed over portions of a ball may in certaincases change the properties of the ball (e.g., how the ball reacts toimpact with the club) and potentially alter flight characteristics ofthe modified ball relative to those of an unmodified golf ball, theimpact of markers as described herein will be minimal as the markers maybe made exceedingly thin and light in comparison to the ball and, formany of the applications for which these exemplary modified ball isintended, these effects are effectively inconsequential or, if need bemay be compensated for in the process of modelling the flight of theball as would be understood by those skilled in the art. For example, inan indoor golf setting, struck balls may travel only a short distance(e.g., 3-4 meters) before hitting a screen. Any effect to the launchcharacteristics of the ball or the flight within that short distancewould be minimal, and the indoor golf system may project the path of theball using ideal golf ball properties in combination with its launchcharacteristics in its calculations. In another example, the ball may bea baseball, and the spin characteristics of the baseball may bedetermined for a pitch or in a batting cage scenario.

According to one exemplary embodiment, a spherical ball is marked tosatisfy a positioning requirement described in detail below. An optionaladditional positioning constraint is also described to further improvethe usage. The requirement and the optional constraint may be met bymany different marker arrangements tailored, for example, to the type ofball being marked. For example, for a golf ball, the markers maycomprise a plurality of circular markers distributed relatively evenlyaround the ball, while for a baseball the markers may be locatedcoextensively with the seams of the baseball, or a portion thereof. Themarkers may be shaped in any manner, however circular or rectangularmarkers may provide a clearer signal in the radar data. For example, atypical marker for a golf ball is circles with a diameter of 2-8 mm, akey dimension of the markers (e.g., a diameter or maximum width) istypically selected to be between 0.25 and 0.5 times the wavelength usedby the radar. It is noted that a marker described herein as circular isnot necessarily a two-dimensional circle, but is rather athree-dimensional shape corresponding to a portion of the surface of asphere (e.g., the outer surface of the ball or an inner sphericalsurface) circumscribed by a circle.

Similarly, a marker described as rectangular may be a two-dimensionalrectangle but may also be a three-dimensional shape formed as a portionof a sphere bounded by the intersection with the sphere of a pyramidhaving an apex at a center of the sphere. As would be understood bythose skilled in the art, this may depend on the structure of theinterior of the ball. Balls having spherical inner layers may havemarkers formed on portions of these spherical layers while a ball thathas a unitary core or a core including a unitary member, may havecircular or other shaped planar markers embedded therein. In thefollowing, these markings may be referred to as the two-dimensionalshapes they approximate as the precise shape of the markers is not asimportant as their pattern of distribution about the surface of theball. A typical number of circular/rectangular markers may be between5-20. The projections of the markers onto an outer surface of the ballwill typically cover 2 to 25% of a surface area of the ball. Thisensures that the markers generate the desired amplification of themodulation signal due to spin on the received Doppler signal. Any numberof markers may be used that satisfy the positioning constraints.Furthermore, although embodiments are described that include allcircular markers or that include all rectangular markers, those skilledin the art will understand that a ball may contain a mixture of markersof various shapes.

A marker positioning requirement is that a distance from every greatcircle around the ball to a nearest one of the markers must be no morethan a predefined minimum distance d. Those skilled in the art shouldnote that, although d is normally positive it can also be negative. Inthe case where d is negative, any great circle around the ball will passthrough at least one marker with a distance d to the non-marked area inthe direction perpendicular to the great circle where the great circleintersects the marker. A great circle (GC) is the path defined by theintersection of a plane going through the center point of the sphere andthe exterior of the sphere, in other words, an equator of the sphere.

A sphere has an infinite number of orientations for a great circle, eachhaving a same diameter as the sphere. Thus, no matter what axis the ballis rotating about, one of the great circles of the ball will define aplane within which the ball is rotating. By ensuring that there is atleast one marker within the defined minimum distance of every greatcircle, the ball according to the present invention, ensures regardlessof the orientation of the axis of rotation of the ball, an oscillatingsignal generated by at least one of the markers will be detected in thereflected radar signal. Thus, according to the positioning requirement,the markers must be positioned so that no great circle may be projectedonto the ball that is not within the distance d of at least one marker.In some embodiments, the distance d may be zero or negative, i.e., everypossible great circle hits at least one marker. Having a d of zero ornegative will in general strengthen the modulation of the Doppler signaldue to spin of the ball. This may be advantageous in situations wherethe time of flight of the ball is very short, such as a golf ball hitinto a net or screen in a simulator environment. However, the distance dmay vary for different balls.

In general, the distance d is significantly smaller than the diameter ofthe ball, e.g. on the order of 0 to ⅕ of the diameter of the ball.Considered a different way, a strip of width d circling the exterior ofthe sphere and having a great circle at its center (i.e., bisecting thestrip) must touch at least one of the markers, regardless of theplacement of the great circle on the ball. In the following, this stripwill be referred to as a great circle of width d. The distance d isdefined as the maximum distance from the great circle to the closestpart of the nearest marker.

FIG. 1a shows a first marked ball 100 with a band 104 of width 2dextending around a great circle GC where the markers 102 satisfy thepositioning requirement—i.e., the markers 102 are distributed over theball 100 so that no great circle GC of the ball does not pass withindistance d of at least one of the markers 102. In this illustrativeexample, the marked ball 100 has six markers 102 on the portion of itsspherical surface shown in this figure. Other markers 102 may be used onthe opposite side of the ball 100 not shown in FIG. 1a . As describedabove, each of the markers 102 has a reflectivity different from theremainder of the ball.

As would be understood by those skilled in the art, this may be achievedby forming markers of a material having a reflectivity (with respect tothe radar signal) higher than that of the ball itself, or by forming alayer of highly reflective material with markers formed as islands notincluding this highly reflective material or from which this highlyreflective material has been removed. As shown, the band 104 surroundinggreat circle GC touches at least one marker 102 and, as can be deducedfrom an analysis of the geometry of the ball 100 and the placement andsize of the markers 102, this is true for any great circle that could bedrawn on the ball 100. To ensure that this condition is met, the markers102 must.

FIG. 1b shows a view of the second marked ball 110 with a band 104surrounding a great circle GC of width 2d drawn thereon that does notsatisfy the positioning requirement. In FIG. 1b , four markers 102 areshown on the spherical surface of the second ball 110, and other markers102 may be included on the opposite side of the ball 110 not shown inFIG. 1b but positioned so that none of them touches the band 104. Asshown, the band 104 surrounding GC does not touch any of the markers102. In this illustrative example, it is assumed that the band 104 alsodoes not touch any of the markers 102 on the opposite side of the ball110. Thus, the marker positioning for the ball 110 does not meet thepositioning requirement and is unacceptable for consistently generatinguseful data for determining spin parameters. For example, the ball 110may rotate in such a manner that no marker 102 is present in an area ofmaximum spin of the ball 110.

An optional additional marker positioning constraint is that, if morethan one marker touches the band of width 2d surrounding a great circle,this group of markers in this embodiment may not be symmetricallydistributed around this great circle within a tolerance of m or theresulting modulations may make it difficult to determine the spin ratebetween choices that are integer multiples of one another—i.e., the samedata may represent 1,000, 2,000 or 3,000 rpm, etc. In other words, forany great circle having two or more markers touching the band of width2d, these markers must not be equally angularly separated from oneanother about the great circle. In the case of two markers touching thegreat circle band, a first marker 102 touching the band of width 2d mustbe separated by at least a distance m from the closest portion of aposition DP diametrically opposed to a second marker 102′ that touchesthe band.

In the case where 3 markers are touching the great circle band, themarkers need to be separated from perfect 120 degree distribution of themarkers on the great circle by a margin m, and a similar constraint willbe applied to any number of markers more than 3 markers touching thegreat circle band. Although the distance m may vary for different balls,in general this distance m is significantly smaller than the diameter ofthe ball (e.g., typically 1/10 of the diameter of the ball or less). Asthe value of m approaches zero, the distance between the marker 102 andthe projection DP of the second marker 102′ will shrink until the marker102 abuts the projection DP.

FIG. 1c shows a view of a third marked ball 120 looking along the axisof rotation of the ball (i.e., a cross-section of the ball 120 is shownincluding a great circle GC defining a path of maximum rotational speedof the ball 120. The ball 120 has multiple markers 102, 102′ contactingthe band of width 2d surrounding a great circle GC and which satisfiesthe additional positioning constraint as described below. Two markers102, 102′ are shown in this example, each having a correspondingdiametrically (relative to the GC) opposite projection (DP, DP′,respectively). The distance 124 between the marker 102 and theprojection DP′ of the marker 102′ is shown as being greater than thedistance m. Those skilled in the art will recognize that geometrydictates that the distance between the marker 102′ and the projection DPof the marker 102 is equal to the distance 124. Thus, the markerpositioning for this particular great circle 104 meets the additionalpositioning constraint discussed above.

FIG. 1d shows a fourth marked ball 130 looking along the axis ofrotation of the ball 130 as in FIG. 1c . The ball 130 includes a firstmarker 102 contacting a band of width 2d surrounding a great circle GCand a second marker 102′ which also contacts the band surrounding GC. Asseen in FIG. 1d , however, the projection DP′ of marker 102′ isseparated from the marker 102 by a distance 134 that is less than m and,in this example, the marker 102 and DP′ actually overlap. In otherwords, the marker 102 is separated from DP′ by a negative distance whichis clearly less than m). Thus, the distancing between the markers 102and the projections 132 violates the additional positioning constraint.In other words, the markers 102 are distributed too symmetrically aroundthe great circle 104. When the markers are positioned too symmetricallyaround the great circle, the received Doppler signal may havecharacteristics that, when applying for example the method described inU.S. Pat. No. 8,845,442, increase the risk that a spin rate will becalculated that is exactly N times higher than an actual spin rate,where N is the number markers touching the great circle. The optionaladditional positioning constraint eliminates this risk. However, aswould be understood by those skilled in the art, other methods may alsobe used to detect whether a calculated spin rate is actually N times thecorrect spin rate and to take appropriate steps to correct this error.

As noted above, various marker arrangements may be used to satisfy thetwo requirements. In general, an uneven number of markers may be used,where each of the markers is separated by minimum distance from anyneighboring markers and are asymmetric relative to any other markers onthe sphere. As will be described in further detail below, the ballmarkings may be on the surface of the ball or on a layer of the ballbelow the surface. When the markings are below the outer surface of theball, a cover material used for the outer surface should besubstantially semi-transparent to the radiation employed by the radar(e.g., microwave radiation) so that this radiation can penetrate theball to reach the marker and be reflected therefrom (or reflecteddifferently from other parts of the ball whether in the same internallayer, on the surface of the ball or embedded in another layer). Whenthe markings for a golf ball are on the outer surface, the markingsshould be highly durable so that they will not come off during useand/or stain the hitting screen in a golf simulator. Normal wear, suchas the wear inflicted on golf ball branding, is expected.

As described above, the markers must have an electrical reflectivity (ormore accurately reflectivity with respect to the radiation generated andgathered by the radar system) different from other areas of the ball,creating a contrast region at different points distributed about thesurface of the ball. For example, the markers may be electricallyconductive in the frequency region of radar being used, thus amplifyingthe modulation signal of a reflected radar signal for a spinning ball.The spin modulation signal can then be used to determine the spin rateand spin axis of the ball even when the flight time for the ball is veryshort.

The exemplary spherical balls may be marked on layers other than theoutermost layer (i.e., external surface) of the ball. A layer of aspherical ball refers to a spherical surface on or within the ballcentered about the center of the ball. These layers may be abstractgeometric divisions of a substantially unitary core, or may be definedby separate layers of materials overlaying one another to form the ball.

According to one embodiment, a ball has one or more first regionscomprised of typical ball materials, e.g., plastic or rubber for a golfball and a plurality of second regions (markers) of material with amicrowave reflection coefficient Γ2. Those skilled in the art willunderstand that the microwave reflection coefficient represents adifference in wave impedance between the air through which themicrowaves are traveling and the particular material of a given regionof the ball. Although the phenomena that determine the precise form ofthe waves reflected from the ball to the radar are complex, it issufficient to understand that the selection of materials havingdivergent values of microwave reflectivity will be most effective ingenerating measurable modulations to make accurate measurements of spincharacteristics. The second regions may be located at any layer of theone- to multi-layer ball. The ball further has, on the same layer as thesecond regions, one or more first regions of material with a microwavereflection coefficient Γ1 that is different than Γ2. As noted above, thesecond regions may be markers in any shape such as circular, rectangularor other shapes with an enclosed geometry. The second regions for agiven ball may each be placed on the same layer or on different layers.Alternatively, the second regions may be comprised of typical ballmaterials, e.g. plastic or rubber for a golf ball while the firstregions in this layer are formed of reflective materials.

According to another embodiment, a ball has the first regions and secondregions as described above, with the additional limitation that thefirst and second regions are both formed of an electricallynon-conductive material having the different microwave reflectionproperties as described above. According to still another embodiment,only the second regions are formed of an electrically non-conductivematerial, while the first regions are formed of an electricallyconductive material. The first regions can be any mixture of materials.Typically for sports balls the material of the ball constructions issubstantially the same for any spherical layer of the ball, however thisis not a requirement. The important thing is that the microwavereflectivity of the second regions is noticeably different from that ofthe first regions, thereby amplifying the spin generated modulation ofthe received Doppler signal

The second regions can be considered as forming the markers discussedabove. The markers may be distributed at a variety of depths within theball so long as the projections of the markers to the outer surface ofthe ball are distributed over the outer surface following the firstpositioning limitation and, optionally, the second positioninglimitation as discussed above. The markers may have any closed shape andneed not be identical. The total area of all the markers togethertypically covers from 1-50% of the surface area of the ball. When themarker is positioned on a layer of the ball that is below the outermostlayer, the area is projected from the center of the ball to the outersurface, and this projected marker area is used for the determination ofwhether the first marker positioning requirement is met.

The microwave reflection coefficient Γ at a transition from one mediumto another depends on the relative differences between the media for oneof the following parameters: the permittivity ε, the permeability μ andthe conductivity σ. If one or more of these 3 parameters are different,the microwave will have some of its electromagnetic field reflected inthe boundary region between the two mediums.

The microwave reflection coefficient Γ between two mediums is given by:Γ=Z1−Z2/Z1+Z2′ where Z1 is the wave impedance in medium 1 and Z2 is thewave impedance in medium 2. The reflection coefficient can be a complexnumber, i.e. a number having a magnitude |Γ| and a phase phase(Γ).

Different materials may be used for the second regions. However,electrically conductive materials such as aluminum, copper and silvergenerate good results. In particular inks containing silver have beenshown to be particularly well suited for the second regions.

According to another embodiment, a spherical ball is marked to satisfyonly one the positioning requirement discussed above. In thisembodiment, the marker positioning requirement is that any great circlearound the spherical ball may be, at maximum, a given distance d awayfrom the closest one of the markers, where the distance d is at maximum⅕ of the diameter of the ball

Similar to above, the markings may be applied on any layer of a typicalmulti-layered ball. For a golf ball, the ball markings may also beapplied on top of the cover, but for more durable markings, it ispreferred to place the markings on one or more of the inner layers ofthe ball. It is noted that the deeper the marking is found in the ball,i.e. the lower the layer the marking is on, the more layers the radarhas to “see through.” The more ball material the microwave radiationneeds to penetrate to reach the marker, the more attenuated the signalwill become, rendering the marking less effective for providing usefuldata. Typically, a compromise may be made by disposing the markingsunder the outer coating but on top of the cover, the cover being on topof the mantle (or core) of the ball. Alternatively, the markings may beplaced directly under the cover. Similar to above, the markings may beapplied at different layers of the ball.

Many different patterns of ball markings may be made to satisfy thepositioning requirement. However, production limitations may limit whatpatterns are feasible. For example, there might be areas of the ballthat are excluded from being marked based on the production equipment.Similar to above, the marking pattern may include circular-shapedmarkings. However, any shape for the markings is feasible, includingrectangular, pentagonal, hexagonal, star-shaped etc. In some productionsetups applying the second regions will happen by stamping the secondregions with, f.ex., conductive ink. For this operation to be costeffective, it may be required to stamp the ball only once. Depending onthe construction of the fabrication machinery this single stamping maylimit the application of ink primarily to a single hemisphere of theball leaving only this half of the ball or even a slightly smaller areaavailable for the inclusion of the second regions. This type ofproduction setup eliminates the extra curing time that might benecessary if more than one application of ink were to be employed (i.e.,eliminating curing time between the first application and a secondapplication, etc.) as well as the time required to reposition the balland perform the second application of ink.

In one embodiment, the marking pattern may be coextensive with a seamrunning around the ball, such as a baseball seam or follow a path thatis similar to such a path even if it is not in the same position as theseams. The marking pattern need not cover the entire seam, i.e., may bea dashed marking pattern, to satisfy the positioning requirement. Aswould be understood by those skilled in the art, the seam of a baseballgenerally forms a continuous curved path along which two cover piecesare joined to one another. Each of the two cover pieces is generallyformed as a planar shape with two rounded ends coupled to one another bya central narrow portion. Thus, when these two cover pieces arestretched over a spherical core, they meet along a continuous curvedpath (see, 302 in FIG. 9) which crosses every great circle around theball.

Other marking patterns may be similar to the seam patterns found on atennis ball, soccer ball, basketball, volleyball, or any other sportsball especially where these seam-type patterns cross every great circlearound a ball. Those skilled in the art will understand that, any of theseam-shaped marking schemes are not applicable only to baseballs orother seamed balls, but may be applied to any sports ball such as a golfball whether it has seams or not. These seam-shaped marking patterns mayalso be dashed, while still satisfying the positioning requirement. Inother embodiments, the markings may be coextensive with a text patternon the ball that is used for e.g. visual branding of the ball. For someballs, these visual text patterns are typically applied on the cover ofthe ball underneath a coating. As noted above, the markings may beapplied on any layer, including visible and non-visible layers. Makingthe markings dashed is one way to reduce the amount material needed forthe marking, and may also decrease risk of deteriorating the adhesiveproperties for the second regions.

When the markings are disposed in the seam-like pattern, an additionalrequirement is imposed. Specifically, the seam-like markings arerequired to have a width between 1/20 to ½ the wavelength of theradiation used by the radar. For example, for a golf ball having adiameter of 42.7 mm and a radar operating at 10-24 GHz (corresponding toa wavelength of 10-30 mm), a suitable width for the markings isapproximately 1-10 mm. However, other radars may be used that operate ina different microwave frequency spectrum, e.g. anywhere from 1-125 GHz.Furthermore, it may be desirable to use larger markers on larger ballseven if the wavelength of the radar signal is the same.

Some examples of the feasible seam patterns are shown in the FIGS. 2-3below. One of the examples shows optional text patterns intended forvisual branding of the ball. The text does not need to be a marked areahaving a different reflectivity, but may be. The visual text patternsare typically applied on the cover underneath a coating, whereas theseam pattern for ball marking can be applied on any layer on the ballbeing visible or not visible.

FIGS. 2a-b show a marked ball 200 with a first marking pattern accordingto one embodiment of the present disclosure. The ball 200 is marked withsix stripes 202 arranged to connect four marking gaps 204 on the ball.The ball 200 is shown transparently to illustrate all the markings 202.As shown, the stripes 202 are not fully connected, but leave the markinggaps 204 surrounding the points at which the stripes 202 wouldintersect. In other embodiments, the stripes 204 may not be completelystraight lines or of equal width. For example, the stripes 204 may betapered, if desired. In general, the markings need to be distributedover the surface of the ball relative to every great circle so that boththe first and second regions generate noticeable radar modulations dueto the spin of the ball.

This can be achieved by making sure that the length of each marker ofthe second regions touching a great circle is sufficient compared to thewavelength and the length of the area of the first regions between themarkings is also sufficient compared to the wavelength to generate thespin modulations regardless of the orientation of the ball and the spinaxis relative to the radar. Sufficient length compared to the wavelengthmeans it is longer than typically 1/20 of a wavelength, but will morepreferably be closer to 0.2 times the wavelength for the second regions.In order to save cost in the application of the second regions, it isdesireable to have the second regions being at maximum 25% of theaccumulated distance along any great circle. This means that f.ex. asecond region formed as an entire equator around the ball is notdesireable, since the great circle that coincides with this equator willhave 100% second regions along the great circle, and as such only veryweak spin modulation will be generated with this particular spin axis.

FIGS. 3a-b show a marked ball 300 with a second marking patternaccording to one embodiment of the present disclosure. The ball 300 ismarked with a baseball seam-style pattern 302 of material havingdifferent reflective properties than the remainder of the ball 300. Theseam need not be continuous, but can be dashed. The ball 300 alsoincludes a brand area 304 for a company to mark the ball with a brand.As discussed above, a brand area may also be used for the reflectivemarkings, if desired.

FIG. 4 shows a system 400 for determining a spin axis of a sports ballaccording to the exemplary embodiments. The system 400 includes a radardevice 402 aimed at a target area through which a sports ball is to passduring at least a part of its flight. In the exemplary system 400, thesports ball is the sports ball 200 discussed above. However, the sportsball 200 may represent any sports ball marked according to the markerpositioning requirements discussed above. The radar 402, in thisembodiment, comprises a transmitter 404 and at least three receivers406. The receivers 406, in this embodiment, are distributed such thatreceivers 406A and 406B are vertically aligned with one another andreceivers 406A and 406C are aligned horizontally with one another.

However, it will be understood by those skilled in the art that thereceivers 406 do not need to be vertically or horizontally aligned solong as the radar device 102 includes three or more receiver antennaswhere a minimum of three of the receiver antennas are not co-linear withone another. It will be understood by those skilled in the art that thereceiver pairs need not be orthogonal to one another. As would beunderstood by those skilled in the art, the geometrical arrangement ofthe separated receivers 406A, 406B, 406C permits analysis of radarsignals reflected from sports ball to the receivers 406A, 406B, 406C toderive an orientation of the spin axis of the ball (an axis about whichthe ball is spinning) at one or more points in time.

The radar 402 may be, for example, a continuous wave Doppler radaremitting microwaves at an X-band frequency (10 GHz) at a power of up to500 milliWatts EIRP (Equivalent Isotropic Radiated Power), thus beingcompliant with FCC and CE regulations for short range internationalradiators. However, in other jurisdictions, other power levels andfrequencies may be used in compliance with local regulations. In anexemplary embodiment, microwaves are emitted at a higher frequencybetween, for example, 5-125 GHz. For more precise measurements at lowerobject speeds, frequencies of 20 GHz or higher may be used. Any type ofcontinuous wave (CW) Doppler radar may be used, including phase orfrequency modulated CW radar, multi frequency CW radar or a singlefrequency CW radar.

It will be understood that other tracking devices such as lidar may beused with radiation in either the visible or non-visible frequencyregion. Current-pulsed radar systems are limited in their ability totrack objects close to the radar device. However, the distance an objectmust be from these pulsed radar systems has decreased over time and isexpected to continue to decrease. Thus, these types of radar may soon beeffective for these operations and their use in the systems of theinvention described below is contemplated. Throughout the application,the tracking of objects is described based on the use of Dopplerfrequency spectrums. As would be understood, these Doppler frequencyspectrums refer to the Doppler spectrum from any type of radar or lidarused.

The system 400 further includes a processing unit 408 which, as would beunderstood by those skilled in the art, may include one or moreprocessors in communication with the radar device 402 (or multiple radardevices) via, for example, a wired or wireless connection. In anembodiment the processing unit 408 includes a computer associated withthe radar device 402.

In the embodiment of FIG. 4, the system 400 is a system for determiningthe spin axis of a ball, e.g. the ball 200, launched within or into atarget area from a given launch position, the target area being within afield of view of the radar 402. As would be understood by those skilledin the art, the target area does not need to be any specially createdarea and the launch position may be any location within or outside thefield of view of the radar 402. When launched into the target area, theball 200 travels along a flight path while spinning in a spin directionaround a spin axis. Those skilled in the art will understand that,although the spin of a golf ball 200 is produced by the striking of thegolf ball 200 with a golf club, the same analysis may be applied to anysports ball whether it has been batted, thrown, kicked, headed, hit byany striking implement (e.g., a baseball bat) etc.

The radar 402 tracks the golf ball 200 as it is launched from the launchlocation (if the launch location is within the field of view of theradar 402) or when the golf ball 200 enters the field of view of theradar 402 and travels along the flight path. As the golf ball 200 moves,radar signals produced by the radar 402 are reflected by the golf ball200 and subsequently received by the radar receivers 406. The spinparameters may then be determined based on the Doppler shift of thereceived signals relative to the transmitted signals. Exemplarycalculations for determining the spin parameters is described in U.S.Patent Publication No. 2019/0282881, the disclosure of which is herebyincorporate by reference.

FIG. 5 shows an exemplary method 500 for determining the spin axis of aspinning ball. In this embodiment, a multi-receiver radar setup isutilized including three receiver antennas 406A, 406B, 406C mounted in aplane. Optionally, additional receiver antennas may be used to increasethe accuracy of the determined positions and to derive athree-dimensional (3D) spin axis. The spinning ball is marked with areflective material in accordance with the marker positioningrequirements discussed above.

In 505, the radar 402 produces signals which are transmitted into atarget area and received after reflection from a spinning golf ball bythe receivers 406A, 406B, 406C, generating a corresponding signalexhibiting a Doppler frequency spectrum. It will be understood that theball may be stationary or moving in any direction relative to the radar402. Due to the spinning motion of the ball, the received Doppler signalis broadened around a value of the Doppler shift associated with thetranslational motion of the ball relative to the radar 402. That is, thereflected signals will be spread across a range of frequenciesreflecting the range of relative velocities of different parts of theball as it is spinning and moving relative to the radar 402. Thereflected signals from the marked regions of the ball, i.e., the regionsof the ball having a different reflectivity than the remainder of theball, will be amplified due to the increased contrast between the areasof enhanced reflectivity and the remainder of the ball 200.

In 510, three-dimensional spin parameters are determined from thereflected signals. The spin parameters include at least a spin rate andan orientation of the spin axis of the spinning ball.

It will be appreciated by those skilled in the art that changes may bemade to the embodiments described above without departing from theinventive concept thereof. It should further be appreciated thatstructural features and methods associated with one of the embodimentscan be incorporated into other embodiments. It is understood, therefore,that this invention is not limited to the particular embodimentdisclosed, but rather modifications are also covered within the scope ofthe present invention as defined by the appended claims.

1. A sports ball configured to enhance detection of spin properties by aradar, comprising: a spherical body having a first reflectivity withrespect to radiation generated by the radar to be used in detecting spinof the ball; and a plurality of markers, each of the markers having asecond reflectivity with respect to the radiation generated by a radarto be used in detecting spin of the ball, the second reflectivity beingdifferent from the first reflectivity, wherein the markers aredistributed on the ball so that every great circle extending around anexterior surface of the ball is within a distance d of a projection onthe exterior surface of the ball of at least one of the markers, andwherein the distance d is less than a radius of the ball.
 2. The sportsball of claim 1, wherein the markers are circular and the projection onthe exterior surface of the ball of each marker comprises a coneextending from a center of the ball to the exterior surface of the ballcircumscribing the marker.
 3. The sports ball of claim 2, wherein atleast one of the markers is a planar disc embedded within the sportsball.
 5. The sports ball of claim 2, wherein at least one of the markersis a portion of a spherical surface within the ball circumscribed by acircle, the spherical surface having the same center as the ball.
 6. Thesports ball of claim 2, wherein the markers are rectangular and theprojection on the exterior surface of the ball of each marker comprisesa pyramid extending from a center of the ball to the exterior surface ofthe ball circumscribing the marker.
 7. The sports ball of claim 6,wherein at least one of the markers is a planar rectangle embeddedwithin the sports ball.
 8. The sports ball of claim 6, wherein at leastone of the markers is a portion of a spherical surface within the ballcircumscribed by a pyramid extending from a center of the ball to theexterior surface of the ball.
 9. The sports ball of claim 1, wherein,when more than one marker is within the distance d of a great circle,the projections of all of these markers on the exterior surface of theball are unequally distributed about the great circle.
 10. The sportsball of claim 9, wherein there are only two markers within the distanced of a first one of the great circles, these markers are notdiametrically opposed to one another.
 11. The sports ball of claim 10,wherein the two markers are not diametrically opposed to one anotherwithin a predetermined tolerance.
 12. The sports ball of claim 9,wherein the markers within the distance d of the great circle areseparated from positions of equal distribution about the great circle byat least a distance m from the projections onto the exterior surface ofthe ball of every other marker whose projection is within the distance dof the great circle.
 13. The sports ball of claim 10, wherein thediametrically opposed position of each marker is a portion of theexterior surface of the ball diametrically opposed to the projection ofthe marker onto the exterior surface of the ball, wherein thediametrically opposed position for each marker has the same size andshape as the projection of the corresponding marker onto the exteriorsurface of the ball.
 14. The sports ball of claim 1, wherein at least aportion of each of the markers extends within a single hemisphere of theball.
 15. A sports ball configured to enhance detection of spinproperties by a radar, comprising: a spherical body having a firstreflectivity with respect to radiation generated by the radar to be usedin detecting spin of the ball; and a spherical layer within the ball ofa material having a second reflectivity with respect to the radiationgenerated by a radar to be used in detecting spin of the ball, thesecond reflectivity being different from the first reflectivity, aplurality of markers formed within the layer at which the material ofthe layer is not present so that the markers have the firstreflectivity, the markers being distributed on the ball so that everygreat circle extending around an exterior surface of the ball is withina distance d of a projection on the exterior surface of the ball of atleast one of the markers, wherein the distance d is less than a radiusof the ball.
 16. A method for manufacturing a sports ball configured toenhance detection of spin properties by a radar, comprising: forming aspherical body having a first reflectivity with respect to radiationgenerated by the radar to be used in detecting spin of the ball; andforming on the sports ball a plurality of markers, each of the markershaving a second reflectivity with respect to the radiation generated bya radar to be used in detecting spin of the ball, the secondreflectivity being different from the first reflectivity, the markersbeing distributed on the ball so that every great circle extendingaround an exterior surface of the ball is within a distance d of aprojection on the exterior surface of the ball of at least one of themarkers, wherein the distance d is less than a radius of the ball.